In the goal of the math problems to get the answers or think for years on a complicated topic? It’s the same Q developers have. Are they paid to type code or create programs?

As a not math person, seems strictly good that AI can solve more problems. If they were important, it can maybe unlock new science. If they had no useful purpose, why did we think about them for years?

> Are they paid to type code or create programs?

The goal is more to understand why something is true than just whether it is true. To oversimplify a lot, it's the difference between industry versus academic motivation. In the former case you have a point, but not so much in the latter. We really need both modes of work going on.

> As a not math person, seems strictly good that AI can solve more problems.

As a math person I think that's probably true, though it's not that simple. We do still have to understand the solutions to the problems, and take time to explore. That's how we figure out what problems should be solved in the first place. Cognitive debt is bad enough in your codebase, but you don't really want it to overwhelm entire academic disciplines.

> If they had no useful purpose, why did we think about them for years?

I don't see a 'we' here. By your own admission you didn't spend years thinking about complicated math topics. So maybe you simply don't see the "purpose". Or maybe no one sees the purpose yet because for some math practical applications take years to discover.

The goal of math is perhaps the answer but also the understanding. One can't use the answers without understanding them, which is a fundamental difference between math and a program. Most modern math isn't applicable in the sense that you just take some result and it gives something practical. The value of math is in understanding it so that it can be properly applied which requires a deep knowledge of why it is so in the first place.

> If they had no useful purpose, why did we think about them for years?

A lot of mathematics is mostly useless, and probably will be for hundreds of years. Some of it ends up being useful, but it's unlikely that much of math like work on geometric langlands will have any applications whatsoever. Math is a service department and the way people teach math best is to be experts in it. In turn, the best way to do that is to develop new math, at least within the context of academia.

Yes, there is some pure math that is used eventually, but I'd say (as someone who worked in pure math for over a decade) that as the results become more specialized and abstract over time, fewer and fewer of them will ever be used.

Every once in a while you see a news article about some math related to physics or something but that's 1/1000 results, if that. The fact is, most modern math research is likely never to be "used".

That doesn't make it useless because maybe we just want to know, but we have to be realistic here...